Adiabatic quantum linear regression.

Area of Science:

• Quantum Computing
• Machine Learning
• Computational Optimization

Background:

• Training machine learning models is computationally intensive on classical computers.
• Optimization problems are a key challenge in machine learning.
• Adiabatic quantum computers show promise for solving complex optimization tasks.

Purpose of the Study:

• To explore an adiabatic quantum computing approach for training linear regression models.
• To formulate the linear regression problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem.
• To compare the performance of the quantum approach against classical methods.

Main Methods:

• Formulating linear regression as a QUBO problem.
• Implementing and testing the QUBO formulation on a D-Wave adiabatic quantum computer.
• Comparing results with a classical Scikit-learn implementation on a desktop workstation.

Main Results:

• The adiabatic quantum computing approach achieved up to a [Formula: see text] speedup over classical methods for larger datasets.
• The quantum approach demonstrated comparable regression error to the classical Scikit-learn method.
• Performance was evaluated using the D-Wave 2000Q and an 8-core Intel i9 processor.

Conclusions:

• Adiabatic quantum computing presents a viable and potentially faster alternative for training linear regression models.
• Quantum approaches can match classical performance in terms of regression accuracy.
• Further research is needed to fully understand the implications of hardware and software implementations on quantum advantage.